ScottPetersonAppeal dot Org has had an article explaining the appellate process up for some time, and includes an explanation of what goes into a direct appeal and what goes into a habeas appeal.
Direct Appeal: Anyone sentenced to death is required to file a direct appeal with the California Supreme Court. This appeal may not be waived. The direct appeal has to do with anything within the court record. It covers things like change of venue, evidentiary issues, juror removal, or any judge's ruling.
Habeas Appeal: While the direct appeal deals with any proceeding that is part of the perfected record, the Habeas is open to almost anything that may challenge a conviction. It may deal with a profound injustice that state law allows, but that our constitution ensures against. Habeas issues would also include new evidence, misconduct by the prosecution, or ineffective counsel for the defendant. Undisclosed bargains or incentives to witnesses can be grounds within this appeal.
The habeas is not automatic. It is filed at the request of the client and the court can deny hearing it without comment.
Click here to read the entire article.